Forty Two wrote:Well, then your model doesn't include matter sucking in space, which is different than you described. Things flowing into black holes is not just a different way of putting it. It's a different concept altogether. So, to correct your theory, you are eliminating the bit about matter sucking in space.

Since it's an hypothesis, and nobody know if it's happening, or the mechanism if it is, then sucking is a reasonable word, as good as any other, to describe something that is hypothetical.

I would define sucking, as creating a partial vacuum. That might be an apt word for the process, if it's happening at all. Or not. It's a bit pointless getting fixated on a word that doesn't really matter at this stage.

The proposal is that matter causes some space to disappear, either by annihilating it or changing it's form.
Other space then moves in to replace it, and more replaces that, etc etc, radiating outwards as an inward flow of space. If there is no "suck" then there would be no flow. It's just a mental picture, there might be other possible mechanisms. I can't think of any offhand, but I'm willing to take suggestions.

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I was trying to model the acceleration of a fluid that has a drain in the centre, to see if it followed the inverse square law. I'm shit at maths so this is probably wrong :
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Take a hypothetical pool with a sunken drain in the centre.
Fixed flow rate down the drain f = Volume V cu metres/T seconds f = V/T
Take two concentric spheres at radius r, inner(ri) and outer (ro). Outer sphere has area Ao, inner has area Ai.

Flow speed at outer = f/Ao Flow at inner = f/Ai Increase in flow speed = f /(Ai-Ao)
Acceleration = (f/Ai-Ao)/T where T is the time taken between the spheres.
So acceleration = (f/Ai-Ao)T

The area of the spheres is proportional to the radius squared. ie 4πro² and 4πri².
So acceleration = (f/(4πro²-4πri²))/T = f/(4πro²-4πri²)T

So the acceleration increases proportionally to the inverse square of the change of radius as you go inwards.
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²

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mistermack wrote:I was trying to model the acceleration of a fluid that has a drain in the centre, to see if it followed the inverse square law. I'm shit at maths so this is probably wrong :
------------------------------------------------
Take a hypothetical pool with a sunken drain in the centre.
Fixed flow rate down the drain f = Volume V cu metres/T seconds f = V/T
Take two concentric spheres at radius r, inner(ri) and outer (ro). Outer sphere has area Ao, inner has area Ai.

I'm not sure why you are comparing velocity to area, but that's not how you subtract fractions. The difference in the flow per surface area between inner and outer is (f(Ao/Ai) - f)/Ao, which == f((Ao/Ai) - 1)/Ao.

Acceleration = (f/Ai-Ao)/T where T is the time taken between the spheres.
So acceleration = (f/Ai-Ao)T

The area of the spheres is proportional to the radius squared. ie 4πro² and 4πri².
So acceleration = (f/(4πro²-4πri²))/T = f/(4πro²-4πri²)T

So acceleration (of the velocity per surface area) is actually = f((Ro/Ri) -1)/4TπRi2

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Ok, I did say I'm shit at maths, and it's probably wrong, I should have said almost certain it's wrong.
It's been a long time, nearly fifty years, and I didn't like maths then. So thanks for pointing it out.
I'm going to have another go, and this will probably be wrong as well.

I started with a fixed flow rate, f cu metres per second. From that I wanted to work out the acceleration of any particle of the fluid, in relation to it's distance r in metres from the intake.

pErvinalia wrote:
I'm not sure why you are comparing velocity to area

I was dividing the area of the sphere by the flow rate (volume per second) to get the velocity. I wanted to subtract the lower outer velocity from the higher inner, to get the increase in velocity, and then divide it by the time T.

Having looked up how to subtract fractions (hopefully properly this time),
f/Ai - f/Ao = f(Ao-Ai)/AiAo

The area of the spheres is proportional to the radius squared. ie 4πro² and 4πri².
So the increase in velocity is f(4πro²-4πri²)/(4πri²)(4πro²) = f(4πro²-4πri²)/16π²ri²ro²

So the increase in velocity divided by the time T is f(4πro²-4πri²)/16π²ri²ro²T metres per sec per second.

Which gives the acceleration for an elapsed period of T seconds. (In the unlikely event that something else isn't wrong.)

How you get from that to acceleration at any point, as T tends to zero, requires calculus I believe, and that's a complete void in my memory. I did actually use maths at university, so I did once know some of it, fifty years ago, although there's no sign of it now.

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It may seem outlandish to postulate that space is flowing past us, straight down into the Earth, but you have to remember that General Relativity is pretty outlandish, and yet it's passed every test so far.

One of the main tenets of GR is that, if you drop an object, it will then follow the path of it's inertial frame of reference, through curved space time. Gravity does not exert a force. The force that you feel, is the Earth pushing you, and changing your motion, and stopping you moving inertially. Which is the same thing as acceleration in my book.

So if you drop a stone off a cliff, you know that it goes straight down, accelerating at 9.81 m/s², and that means that all genuine inertial frames of reference at the Earth's surface are also accelerating straight down at 9.81 m/s² relative to the surface of the Earth. Because any massive object will do the same thing.

That's what leads me to suggest that space itself is doing the same thing. Would it not be stranger, if it wasn't?
But of course, GR says that the falling stone off the cliff is not accelerating. Well, either the stone is accelerating, or the cliff is. So if the stone isn't, then the cliff is.

And according to GR, the cliff is not in free fall, it's not moving inertially through curved space time, so it's accelerating.

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On the scienceforum thread, Strange did the calculation to compare how time dilation caused by space falling, as I'm proposing, would compare to the established gravitational time dilation formula.

He wrote "I haven't tried it but I think if you apply the Lorentz transform to the equation for escape velocity (which is the same as the speed when falling from infinity, which is your 11.186km/s) then you should end up with the equation for gravitational time dilation."

And then produced this calculation :

What that shows is that IF space was whizzing past us on the surface, at 11.186km/sec, it would produce exactly the same time dilation, as we can measure due to gravity.

So you can either postulate two totally different possible types of time dilation, that just happen to produce the identical result, or that there's just one type of time dilation, which of course would naturally produce the same figures.

Occam's razor and all that. The second seems more logical.

I've still had no refutation over there, after more than two weeks.
That in itself is a bit of a record for that place. Stuff is usually destroyed in minutes, or hours at the most.

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I understand the individual bits that make up your posts, but the whole makes absolutely no sense to me. I really have no idea what it is that you are trying to convey. I can't tell if you are operating at a higher realm than the rest of us, or you are wibbling your little heart out. I'm going to stick with the latter until you start saying something that makes sense.

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I think I know what the flaw was (aside from your mixing up inertial frames with non-inertial frames). Under a gravity model it is perfectly understandable how the escape velocity from behind an event horizon can be greater than the speed of light. But under your 'space flows' model it is impossible, as it would require the flow of space to be moving at or above the speed of light.

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pErvinalia wrote:I think I know what the flaw was (aside from your mixing up inertial frames with non-inertial frames). Under a gravity model it is perfectly understandable how the escape velocity from behind an event horizon can be greater than the speed of light. But under your 'space flows' model it is impossible, as it would require the flow of space to be moving at or above the speed of light.

Well, that's not a bad try. You are at least getting closer to understanding the concept.
However, if you read the published river model links, you will see that the speed of light doesn't apply to space in relativity. They actually use the words that space can do what it wants. And it's exactly that, a river of space falling into a black hole faster than light, that they say causes the event horizon to exist in the first place.

I wasn't aware of that myself till someone mentioned it on the science forum. It could have been that that made me drop it six months ago, I still can't remember.

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Eyes glazed over trying to read that paper. It's not mobile friendly, so each line is chopped to bits. I'm sure they've thought of this, but I'll point it out nonetheless.. If light moves relative to the framework of space, then that means the speed of light (in different parts of space) is not invariant. Which is of course incompatible with relativity. Not sure how they wibble their way out of that one, but I couldn't read enough to find out.

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